All people, without exception, have a pretty good
idea of what "hardness" means in the context of materials properties.
Extremely few people, however, have a decent notion of what the terms
"yield stress" or "maximum elongation" tells us about
materials properties.

Ironically, while the two latter properties are
well-defined, hardness is not!

Yield stress,
as we know, can be measured in precisely
defined ways, and can be expressed in terms of basic material properties.

Hardness is
different. It is not uniquely defined, and that means there is no unambitious
way of measuring it. There are only some recipes - that's why we have several hardness scales
in parallel.

Essentially, there are two types of basic hardness
measurement set-ups (plus some more unusual principles).

1. Measure the size
of an indentation made by some indenter under a known load. The following
hardness tests use this principle:

In the "Materials in Action" series,
"Structural Materials", page 100, the scales are compared
(which is not easy).

Here we usually use the Vickersscale. It runs from 0 to about
3000; the unit is essentially that of stress (Pa); but the
numbers are given in outdated units:

In the "Materials in Action" series you will find an
unusual unit: "kgf", which is kilogram-force, which is something different from a
"kg", because that was and is a mass. Nevertheless, the unit
for the hardness is kg/mm2; what is meant is the force that a
mass of one kg experiences in the gravitational field of the earth. In
German the unit "kilopond" (kp) was used; it's the same thing.
Of course we
have1kg/mm2»
10N/106 m2 = 105 Pa

Here is a table with some Vickers hardness data:

Material

Vickers hardness

Material

Vickers hardness

Material

Vickers hardness

Sn

5

Limestone

250

Polypropylene

7

Al

25

MgO

500

Polycarbonate

14

Au

35

Window glas

550

PVC

16

Cu

40

granite

850

Epoxy

45

Fe

80

quartz

1200

Mild steel

140

Al2O3

2500

Hardened steel

900

WC

2500

Hardness measures in some lumped way a combination
of elastic, plastic, and fracture properties, i.e. it combines somehow Yield
stress, Youngs modulus and fracture parameters.

There is, however, no unique formula giving the hardness
number as a function of the primary parameters.

The best one can do is to provide some approximate
relations for certain classes of materials.

For relatively soft metals and for steel, respectively, there
is a very simple relation between the Vickers Hardness
HV and the yield
stress RP or the tensile strength
RM

HV

»

3 RP

"soft" metals

3.2 RM

steel

Of course, you have to express the strength parameters in
kg/mm2, too

This makes life easier and explains why we have
not much dealt with hardness here: For our materials of interest, it is
essentially the same as the much better defined parameters governing plastic
deformation.

Life would be even more easier, if most scientists would use
the same hardness scale. Of course, they don't, so here is an approximate
conversion, adopted form the "Materials in Action " Series
already mentioned.